Give a step-by-step explanation of how to evaluate the determinant. Match sequence of steps. $$\left| \begin{array} { c c c }
5 & 0 & 4 \
1 & - 4 & 6 \
7 & 0 & 9
\end{array} \right|$$
-First step
A) $\left| \begin{array} { c c c }
5 & 0 & 4 \
1 & - 4 & 6 \
7 & 0 & 9
\end{array} \right| = ( 0 ) ( - 1 ) ^ { 2 + 1 } \left| \begin{array} { l l }
1 & 6 \
7 & 9
\end{array} \right| + ( - 4 ) ( - 1 ) ^ { 2 + 2 } \left| \begin{array} { l l }
5 & 4 \
7 & 9
\end{array} \right| + ( 0 ) ( - 1 ) ^ { 2 + 3 } \left| \begin{array} { l l }
5 & 4 \
1 & 6
\end{array} \right|$
B) $\left| \begin{array} { c c c }
5 & 0 & 4 \
1 & - 4 & 6 \
7 & 0 & 9
\end{array} \right| = ( 0 ) ( - 1 ) ( - 33 ) + ( - 4 ) ( 1 ) ( 17 ) + ( 0 ) ( - 1 ) ( 26 )$
C) $\left| \begin{array} { c c c }
5 & 0 & 4 \
1 & - 4 & 6 \
7 & 0 & 9
\end{array} \right| = 0 - 68 + 0 = - 68$

Question

Give a step-by-step explanation of how to evaluate the determinant. Match sequence of steps. $$\left| \begin{array} { c c c } 
5 & 0 & 4 \
1 & - 4 & 6 \
7 & 0 & 9
\end{array} \right|$$
-First step
A) $\left| \begin{array} { c c c } 
5 & 0 & 4 \
1 & - 4 & 6 \
7 & 0 & 9
\end{array} \right| = ( 0 ) ( - 1 ) ^ { 2 + 1 } \left| \begin{array} { l l } 
1 & 6 \
7 & 9
\end{array} \right| + ( - 4 ) ( - 1 ) ^ { 2 + 2 } \left| \begin{array} { l l } 
5 & 4 \
7 & 9
\end{array} \right| + ( 0 ) ( - 1 ) ^ { 2 + 3 } \left| \begin{array} { l l } 
5 & 4 \
1 & 6
\end{array} \right|$ 
B) $\left| \begin{array} { c c c } 
5 & 0 & 4 \
1 & - 4 & 6 \
7 & 0 & 9
\end{array} \right| = ( 0 ) ( - 1 ) ( - 33 ) + ( - 4 ) ( 1 ) ( 17 ) + ( 0 ) ( - 1 ) ( 26 )$ 
C) $\left| \begin{array} { c c c } 
5 & 0 & 4 \
1 & - 4 & 6 \
7 & 0 & 9
\end{array} \right| = 0 - 68 + 0 = - 68$

Quizplus · Accepted Answer

The first step in evaluating the determinant of a 3x3 matrix involves expanding it along a row or column (typically chosen for having zeros to simplify calculations). Option A correctly applies this expansion along the second row, using the formula for the determinant of a 3x3 matrix, which involves multiplying the elements of the row or column by the determinant of the 2x2 matrix that remains after removing the row and column of each element, and adjusting for sign based on position.

Give a Step-By-Step Explanation of How to Evaluate the Determinant ∣5041−46709∣\left| \begin{array} { c c c } 5 & 0 & 4 \\1 & - 4 & 6 \\7 & 0 & 9\end{array} \right|​517​0−40​469​​

Give a Step-By-Step Explanation of How to Evaluate the Determinant $\left| \begin{array} { c c c } 5 & 0 & 4 \\1 & - 4 & 6 \\7 & 0 & 9\end{array} \right|$